Dark and Bright Solitons in Left-Handed Nonlinear Transmission Line Metamaterials

The existence of a solitary wave and soliton solutions in a nonlinear (NL) left-handed (LH) transmission line (TL) loaded with nonlinear varactor diodes is demonstrated rigorously for the first time and corresponding closed-form solutions are provided. These solutions are modulated dark and a bright solitons for the cases of heterostructure barrier varactor (HBV) and hyperabrupt junctions varactor (HJV) diodes, respectively. It is shown that NL LH TLs, despite their very different dispersion response, may support solitons identical to those in optical fibers in their normal dispersion regime, in contrast to RH TLs which can support only non-modulated (KdV) and bright solitons. Due to this equivalence, it maybe be anticipated that NL LH TLs will lead to several novel and unique microwave applications, such as UWB pulse shapers and compressors, which will be developed by transposition of concepts from the photonics.